Problem

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Problem 31 Using Proportions
Three brothers, Bob, Dan, and Mark, receive a
gift of 45,000 zeds from their father. The money
is shared between the brothers in proportion to
the number of children each one has. Bob has 2
children, Dan has 3 children, and Mark has 4
children. How many zeds does Mark get? A.
5000 B. 10,000 C. 15,000 D. 20,000

• PRAXIS - WI
• Jon Hasenbank
• Rachel Klinner
• Katie Schank
• Anusack Banuvong
• Traci Leis

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DPI Standards

• B.12.2 Compare real numbers using ratios,
  proportions, percents, and rates of change.
• B.12.4 Model and solve a variety of mathematical
  and real-world problems by using algebraic
  expressions, equations, and inequalities.
• Other Relevant Knowledge how to organize
  information and set up a proportion, how to solve
  a proportion, how to use basic algebra, how to
  use basic operational skills

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Three brothers, Bob, Dan, and Mark, receive a
gift of 45,000 zeds from their father. The money
is shared between the brothers in proportion to
the number of children each one has. Bob has 2
children, Dan has 3 children, and Mark has 4
children. How many zeds does Mark get? a.
5000 b. 10,000 c. 15,000 d. 20,000

• Feedback
• a. Sorry, that is incorrect. The money will
  essentially be split nine ways but the number of
  children Mark has determines the total number of
  zeds that Mark receives.
• b. Sorry, that is incorrect. 10,000 is 2/9 of
  45,000, so this amount goes to Bob because he has
  2/9 of the children.
• Sorry, that is incorrect. Remember that the
  money is not split equally among the sons because
  each has a different number of children.
• d. Correct! Mark has 4/9 of the children, so
  he will receive 4/9 of the total . . . And 4/9 of
  45,000 is 20,000 zeds!

Total Pot of Money 45,000
Dan
Bob
Mark
Number of children Amount of Money
9 45,000 (This
proportion should appear under each brothers
circle above. As students drag the diamonds into
the circles, the numbers should adjust on the
proportions as well.)
1 child/ 5,000
Find the fraction of the overall number of
children that are Marks. This is the fraction
of the total gift of money that Mark will receive.
Using Proportions
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Tutorial
Three brothers, Bob, Dan, and Mark, receive a
gift of 45,000 zeds from their father. The money
is shared between the brothers in proportion to
the number of children each one has. Bob has 2
children, Dan has 3 children, and Mark has 4
children. How many zeds does Mark get? A.
5,000 B. 10,000 C. 15,000 D. 20,000
1. Because the inheritance is in proportion to
the number of children each brother has, lets
set up a proportion part a part b whole a
whole b Let each part of the proportion fly in
to form the proportion.
Using Proportions
5
Tutorial

• Then we can substitute numbers from our problem
  for the parts and wholes. Mark has four parts
  out of the total nine children. And we are
  looking for the amount of zeds, x, he will
  receive out of the total 45,000 zeds.
• 4 x
• 9 45,000
• Each component should fade into the numbers one
  at a time until the proportion looks like the one
  above.
• Then display an explanation which can pop up
  simultaneously next to each component of this
  proportion for example
• 4 the number of children Mark has (part),
• 9 the total number children (whole),
• x the amount of money that Mark will receive
  (part),
• 45,000 the total amount of money being
  inherited (whole)

Three brothers, Bob, Dan, and Mark, receive a
gift of 45,000 zeds from their father. The money
is shared between the brothers in proportion to
the number of children each one has. Bob has 2
children, Dan has 3 children, and Mark has 4
children. How many zeds does Mark get? A.
5,000 B. 10,000 C. 15,000 D. 20,000
Using Proportions
6
Tutorial
3. Next we must find a common denominator. In
this case it is 45,000, so we must multiply the
top and bottom of the 4/9 by 5,000. Now make
(5,000) slide in next to both the 4 and the 9.
After a second or two, make the 4(5,000) blend
together and turn into 20,000. Also make the
9(5,000) blend together and turn into 45,000.
Three brothers, Bob, Dan, and Mark, receive a
gift of 45,000 zeds from their father. The money
is shared between the brothers in proportion to
the number of children each one has. Bob has 2
children, Dan has 3 children, and Mark has 4
children. How many zeds does Mark get? A.
5,000 B. 10,000 C. 15,000 D. 20,000
Using Proportions
7
Tutorial
4. And so our answer is D. 20,000 zeds. Make
the two sides of the proportion blend together
and turn into x 20,000 so that we can see
that they are equal to each other, and the answer
must be 20,000.
Three brothers, Bob, Dan, and Mark, receive a
gift of 45,000 zeds from their father. The money
is shared between the brothers in proportion to
the number of children each one has. Bob has 2
children, Dan has 3 children, and Mark has 4
children. How many zeds does Mark get? A.
5,000 B. 10,000 C. 15,000 D. 20,000
Using Proportions
8
Three brothers, Bob, Dan, and Mark, receive a
gift of 45,000 zeds from their father. The money
is shared between the brothers in proportion to
the number of children each one has. Bob has 2
children, Dan has 3 children, and Mark has 4
children. How many zeds does Mark get? A.
5000 B. 10,000 C. 15,000 D. 20,000
Using Proportions
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A. Four sisters (Alexis, Eliza, Amanda, and
Jessica) received an inheritance of 30,000 when
their mother passed away. The money was shared
in proportion to the number of children each one
has. Alexis has two children, Eliza has one
child, Amanda has no children, and Jessica has
three. How much money did Alexis receive?
A. 7,500
C. 10,000
B. 5,000
D. 15,000
Feedback
A. Sorry, that is incorrect. Remember that the
money is not shared equally among the sisters!
C. Correct!
B. Sorry, that is incorrect. Each grandchild
would receive this amount, but Alexis has TWO
children.
D. Sorry, that is incorrect. This is the amount
that Jessica would receive, not Alexis.
Using Proportions
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B. Three sisters (Pam, Linda, and Teresa) won
the lottery for 5,000,000, after purchasing a 1
ticket. Since they did not each pay equal
amounts for the original 1 ticket, they decided
to split the prize money in proportion to the
amounts that each paid for the winning ticket.
Pam paid 0.45, Teresa paid 0.35, and Linda paid
0.20. How much of the 5,000,000 did Pam
receive?
C. 1,666,666.67
A. 2,250,000.00
B. 1,000,000.00
D. 450,000.00
Feedback
A. Correct! This is 45 of the total 5 million,
the amount Pam deserves to receive.
C. Sorry, that is incorrect. Remember they did
not share the money equally.
B. Sorry, that is incorrect. 1,000,000 is 20
of the total, the amount Linda should receive.
D. Sorry, that is incorrect. 450,000 is not
45 of 5 million.
Using Proportions
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C. Four brothers (Jeremy, Jaden, Cody, and
Logan) won the lottery (a grand prize of
50,000!) with a 1.50 ticket that they purchased
together. They decided to split the money in
proportion to the amount of the ticket that each
paid for. Jeremy received 25,000, Jaden and
Cody each received 10,000, and Logan received
5,000. How much of the original 1.50 ticket
did Logan pay?
A. 0.15
C. Approximately 0.38
B. 0.75
D. Approximately 1.13
Feedback
A. Correct!
C. Sorry, that is incorrect. Remember that
these brothers did not all pay the same amount.
B. Sorry, that is incorrect. This is the amount
of the ticket that Jeremy paid for half of it
not the amount Logan paid for.
D. Sorry, that is incorrect. Logan didnt
receive 75 of the profits, so he didnt pay for
75 of the original ticket either.
Using Proportions
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D. Sarah decided to prove to her friends that
the majority of MMs in a bag are brown, as she
firmly believes. She sorted them by color and
found that the bag contained 110 MMs total.
Just as she suspected, 56 of the MMs in the
bag were brown. How many brown MMs were there?
A. 30 MMs
C. 54 MMs
B. 56 MMs
D. Approximately 62 MMs
Feedback
A. Sorry, that is incorrect. Remember to find
56 of the total number of MMs.
C. Sorry, that is incorrect. Remember to find
56 of the total number of MMs.
B. Sorry, that is incorrect. Remember, there
were 110 MMs in the bag, not 100!
D. Correct!
Using Proportions
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E. Ellen wanted to prove that there are very few
red MMs in most bags. Out of a bag of 110
MMs, Ellen found 7 red ones. What percentage
of the total number of candies was red?
A. 10
C. .0636363636
B. 6.36363636
D. 7
Feedback
A. Sorry, that is incorrect. Find the number of
red MMs to the total number in the bag.
C. Sorry, that is incorrect. Remember to move
the decimal point when you convert to percentages.
B. Correct!
D. Sorry, that is incorrect. Remember, the bag
contains 110 candies, not 100.
Using Proportions
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F. Sarah has a bag of 200 MMs. She decided to
share with her friends and gave Amy all the green
ones (15 of the total), Megan all the yellow
ones (13), Jaclyn all the orange ones (10),
Kelly all the red ones (6), and Ellen took all
the brown ones (56). How many MMs out of the
original 200 did Megan get?
C. 13 yellow MMs
A. 26 yellow MMs
B. 20 yellow MMs
D. 40 yellow MMs
Feedback
A. Correct!
C. Sorry, that is incorrect. Remember to take
13 of 200, not 100.
B. Sorry, that is incorrect. Jaclyn received 20
MMs, not Megan.
D. Sorry, that is incorrect. Remember the MMs
were not shared equally among the friends.
Using Proportions
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G. Berry Berry Cereal Company has decided to
donate 5 of their profits to a disaster relief
organization. Another 10 of their profits will
be given to a homeless shelter. Last year Berry
Berry Cereals profits totaled 250,000. How
much of this money was donated to charity?
A. 83,333.33
C. 12,500.00
B. 16,666.67
D. 37,500.00
Feedback
A. Sorry, that is incorrect. Remember that the
money was not divided evenly by three.
C. Sorry, that is incorrect. This is the amount
donated to the disaster relief organization.
B. Sorry, that is incorrect. We need to find 15
of 250,000.
D. Correct!
Using Proportions
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H. Berry Berry Cereal Company has decided to
donate 5 of their profits to a disaster relief
organization and another 10 of their profits to
a homeless shelter. Last year, they gave 15,000
to the disaster relief organization. What was
their profit that year?
A. 300,000
C. 250,000
B. 100,000
D. 150,000
Feedback
A. Correct!
C. Sorry, that is incorrect. Check your
calculations.
B. Sorry, that is incorrect. This would be the
total profits if the company had given 15 of
profits to this organization.
D. Sorry, that is incorrect. Remember that the
disaster relief organization receives 5 of the
profits.
Using Proportions
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I. Kelly and Joey are taking a trip from Madison
to New Orleans. The entire trip should take 16
hours. Their first stop was in St. Louis, 5
hours after leaving Madison. What percentage of
the distance is yet to be traveled?
C. 11
A. 68.75
B. 31.25
D. 66.67
Feedback
A. Correct!
C. Sorry, that is incorrect. We are trying to
find the percentage equivalent to 11 hours left
out of 16 total hours.
B. Sorry, that is incorrect. Remember that we
are trying to find the distance YET to be
traveled.
D. Sorry, that is incorrect. This is the
equivalent of 5/15, not 5/16.
Using Proportions
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J. Kelly and Joey are taking a trip from Madison
to New Orleans, which should take a total of 16
hours. After leaving from Madison, their first
stop was in St. Louis, 5 hours later. Their
second stop was in Memphis, 9 hours from Madison.
What percentage of the distance was covered
between St. Louis and Memphis?
C. 43.75
A. 4
D. 25
B. 56.25
Feedback
A. Sorry, that is incorrect. They drove 4 hours
between St. Louis and Memphis, not 4 of the trip.
C. Sorry, that is incorrect. This is the
percentage of the trip left to be traveled after
they leave Memphis.
B. Sorry, that is incorrect. Remember that we
are working with the distance BETWEEN St. Louis
and Memphis.
D. Correct!
Using Proportions